3 Answers
3

Normal chord notation specifically avoids octaves so that the performer isn't bogged down and can arrange the chord as they please.

If you're spelling out a particular arrangement of a chord, just draw the notes in standard notation on the staff and put the chord without octaves in normal form above the staff.

If you must spell out each pitch's octave and the notes as text, use the standard note+octave notation - C4 is middle C, C3 is an octave down, etc.

If you're sticking with your interval notation, the P is usually understood for 1, 4, and 5. You usually only need to prefix a m or M for 2, 3, 6, and 7. Tritone is the weird one - usually written (I think) as aug4/dim5 or just tritone.

I dont know what you mean with "P" (do you mean 'T'=Tonika?) but if those numbers should stand for oktaves, here are some rules to become understandable in the world:
Capital letters (majuskels) stand for chords, small letters (minuscels) for tones:

Here are some rules. If you get the system, all becomes pretty simple.

In chord notation, every number above 6 stands for tones that you add, every number blow for tones that substitute.

Add m to the basetone, if you want a minor third

Add ° or 0, if you want 2 stacked small terces, c - e♭ - g♭

Add +, if you want two stacked big terces, c - e - g♯

5 stands for chords without a third (powerchord)

3 and 3- stand forn chords without a quint

4 and 2 substitue the third.

6 substitutes the 5

7 is a small one.

Add Δ to the base, if you want a major sept. You may write j7 if you dont find the letter delta in your charmap.

So E♭Δ9 stands for e♭ - g - b♭ - d - f

If you want to invert, just write down the bass-tone (captial letter because it is part of a chord) after a slash:

E♭Δ9/G : first inversion

E♭Δ9/B♭ : second inversion

E♭Δ9/D : third inversion

E♭Δ9/F : forth inversion

The seventh (sept) has some specials that depend on how you use the system and are not universally agreed.

A 07 should be a diminished chord with the added minor seventh: c - e♭ - g♭ - b♭, that chord is called a half-diminished chord.

A ø denotes a fully diminished chord (c - e♭ - g♭ - b♭♭) which has a diminished sept (♭7): It 'goes thru the system', because you can invert it as you like as 3 minor terces have the surrounding interval of an octave, so effectively there are just 3 fully diminished chords in total, each with 4 equally sounding inversions. Sadly, as ø looks like something that is half cut thru, it became misunderstood as the half-diminished chord, with should be 07=0+7. So if you see 07 or ø, you have to make an educated guess;)

Yes, thats a problem. In the 'code' is 07 = 0+7. but you may also state that 7 = 'a minor terce added to a triad'. The first way would bring you to 7 is always a small sept, while the other road leads to 7 is either a small sept or a diminished one depending on the chord below. In either system, the ø is used for 'the other chord', which really makes it a mess. For the logic of the system (denote everything that differ from the major triad), its better to have Em07 = Em7 with a diminished third and Emø as a special way to write the harmonically wrong Em06, but sadly, both is used in the wild:/
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rhavinJan 25 '14 at 3:01

Chord symbols themselves are for are not exact notation. For example I if I gave you the progressions C Am Dm/F G7, all it is telling you is to play those chords not how to play them. If you want a specific voicing for a chord, typically you would write it in standard notation.

Intervals typically don't get chord symbol with the exception of Perfect 5th(power chords) and octaves because intervals are not chords. You can get away with using chord notation for certain intervals. For example if you had a C and an A, you could call it a Am/C because the 5th isn't the most important note in a triad. There is notation to analyze intervals, but the not for directing someone to play them. Again it is best to write the desired notes in standard notation.